Appears in collection : 100 (102!) Years of the Ising Model

As a counterpoint to ``be wise and discretize’’, continuous extensions are relevant and provide useful perspective. They occasionally pose challenges but also yield new tools. Examples of both may be found in: the contact process as extension of discrete percolation, long-range 1D Ising and percolation models, the quantum Ising model, quantum spin chains, influence propagation in the random-field Ising model estimated through a stopping time argument, extensions of discrete random height functions, and new results for the Villain O(2) spin system though its metric graph representation.